The game is euchre which uses a 24 card deck (Ace through 9). The dealer picks up the King of diamonds, names diamonds trump, and discards the King of hearts. Dealer holds the K-10-9 diamonds, Ace spades, and 9 of clubs. Q1. What is the probability that his partner does not hold either the Jack of hearts or the Jack of spades? Q2. What is the probability that his partner holds one of the red Jacks? Q3. What is the probability that the partner holds both of the red Jacks?
To answer these questions, we need to understand the concept of probability and the basic rules of euchre. Let's break down each question step by step:
Q1. What is the probability that his partner does not hold either the Jack of hearts or the Jack of spades?
To find the probability, we need to know the number of favorable outcomes and the total number of possible outcomes. Here's how you can calculate it:
- Total number of possible outcomes: In a 24 card deck, there are a total of 24 cards.
- Number of favorable outcomes: We need to determine how many cards are left in the deck after the dealer's hand has been dealt.
The dealer holds 5 cards (K-10-9 of diamonds, Ace of spades, and 9 of clubs), and two cards have been discarded (King of diamonds and King of hearts). Therefore, there are 24 - 7 = 17 cards remaining in the deck.
Now we need to determine the number of cards that are neither the Jack of hearts nor the Jack of spades. In a standard euchre deck, there are four suits, each with a Jack. So we have three remaining Jacks (Jack of diamonds, Jack of clubs, and Jack of spades).
Since there are only three Jacks remaining out of the 17 cards, the probability that his partner does not hold either the Jack of hearts or the Jack of spades is 3/17.
Q2. What is the probability that his partner holds one of the red Jacks?
To find this probability, we consider the favorable outcomes (partner holds one of the red Jacks) over the total possible outcomes (all remaining cards).
- The number of favorable outcomes: There are two red Jacks remaining (Jack of diamonds and Jack of hearts).
- The total number of possible outcomes: There are 17 cards remaining in the deck after the dealer's hand and the discarded cards.
Therefore, the probability that his partner holds one of the red Jacks is 2/17.
Q3. What is the probability that the partner holds both of the red Jacks?
To calculate this probability, we need to consider the favorable outcomes (partner holds both red Jacks) over the total possible outcomes.
However, in this scenario, it is not possible for the partner to hold both red Jacks because one of them (Jack of hearts) was discarded by the dealer. Therefore, the probability of the partner holding both red Jacks is 0.
So, to recap:
Q1. The probability that his partner does not hold either the Jack of hearts or the Jack of spades is 3/17.
Q2. The probability that his partner holds one of the red Jacks is 2/17.
Q3. The probability that his partner holds both of the red Jacks is 0.